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Full Idea
One is the Number which belongs to the concept "identical with 0".
Gist of Idea
One is the Number which belongs to the concept "identical with 0"
Source
Gottlob Frege (Grundlagen der Arithmetik (Foundations) [1884], §77)
Book Ref
Frege,Gottlob: 'The Foundations of Arithmetic (Austin)', ed/tr. Austin,J.L. [Blackwell 1980], p.90
A Reaction
This follows from Idea 8653, which defined zero. Zero is the number of a non-existent set, and one is how many sets you have when you have only got zero. Very clever.
Related Idea
Idea 8653 Nought is the number belonging to the concept 'not identical with itself' [Frege]
| 7485 | For Pythagoreans 'one' is not a number, but the foundation of numbers [Pythagoras, by Watson] |
| 12074 | The one in number just is the particular [Aristotle] |
| 9894 | A unit is that according to which each existing thing is said to be one [Euclid] |
| 12488 | The idea of 'one' is the simplest, most obvious and most widespread idea [Locke] |
| 8636 | We can say 'a and b are F' if F is 'wise', but not if it is 'one' [Frege] |
| 8654 | One is the Number which belongs to the concept "identical with 0" [Frege] |
| 14421 | Discovering that 1 is a number was difficult [Russell] |